Dual networks and self-checking dividers

Methods of establishing dual network pairs and self-checking dividers from a string of 12 nominally equal resistors permanently connected in series using short-circuiting links between nodes are described. Dual networks that can be generated from a string of 11 nominally equal resistors, permanently connected in series with Hamon star junctions by joining one or more nodes together with one or more zero-resistance links, are established. These networks are then coupled together to form all possible three-terminal self-checking divider networks attainable using a total number of resistors from 2 to 12. There are 58269 physically different dual pairs using 11 resistors, comprising 3733 numerically different ratios. Correspondingly there are 79053 self-checking dividers with 4367 numerically different ratios